A few hours ago I read about the aria-label attribute, which:
Defines a string value that labels the current element.
But in my
In the example you give, you're perfectly right, you have to set the title attribute.
If the aria-label is one tool used by assistive technologies (like screen readers), it is not natively supported on browsers and has no effect on them. It won't be of any help to most of the people targetted by the WCAG (except screen reader users), for instance a person with intellectal disabilities.
The "X" is not sufficient enough to give information to the action led by the button (think about someone with no computer knowledge). It might mean "close", "delete", "cancel", "reduce", a strange cross, a doodle, nothing.
Despite the fact that the W3C seems to promote the aria-label rather that the title attribute here: http://www.w3.org/TR/2014/NOTE-WCAG20-TECHS-20140916/ARIA14 in a similar example, you can see that the technology support does not include standard browsers : http://www.w3.org/WAI/WCAG20/Techniques/ua-notes/aria#ARIA14
In fact aria-label, in this exact situation might be used to give more context to an action:
For instance, blind people do not perceive popups like those of us with good vision, it's like a change of context. "Back to the page" will be a more convenient alternative for a screen reader, when "Close" is more significant for someone with no screen reader.